GIBBS' PAPERS I AND II 49 



which must be used and the equation must be between P, V, T. 

 Such an expression as 



pv 



— must be the same for all substances. 



PcVc 

 tc 



If m denote the mass and M the molecular weight we have 



p t V pci'cM p V M 

 Pc tc Vc Um ' tm 



equal for all substances. (The last two expressions must be 

 measured in the same units for the different substances, but the 

 first three may be measured in any units.) So, too, 



t_ /dp\ ^ t_ /dri\ ^ 1 /dQ\ 

 p\dt/v p \dv/t p \dv/t 



would be alike. Also 



V \dt/p V \dp/t V 



'dQ' 

 \dp/ 



For coexistent phases there would be certain expressions in- 

 variant of the substance. 



p\dt/v p\dv/t pv2 — Vi 

 As f 1 = ^2 we may state that the ratios 



(€2 - ei) : ^(772 - Vi)-Piv2 - Vi) 



are the same for all substances when 2 and 1 stand for the vapor 

 and the liquid phase, each in the presence of an infinitesimal 

 quantity of the other. By examining data for different sub- 

 stances one may see how far the departure from constancy is 

 and thus gain some idea of in how far it might be hopeful to seek 

 for equations of state which would satisfy the requirement that 

 in proper units the equation should be the same for the different 

 substances. 



